Statistical methodology in numismatic studies

The note is concerned with the statistical methods applied to numismatic studies with particular reference to a previously published study of the trace-element composition of Augustan coins (Carter, G. F. (1978), Journal of Archaeological Science5). In particular, it is shown that the grouping procedure proposed by Carter is likely to produce too many “significant” groups. The compositional differences between predefined groups based on issue and year of manufacture are also considered. Multivariate techniques are used to investigate these differences and the advantages of this approach in comparison to the inspection of univariate plots are pointed out.     

Spread-Es structure producing apparent small scale structure in the F-region

When transmitting on 5.8 MHz the Bribie Island HF radar array synthesizes a beam that is 2.5 wide. The beam can be steered rapidly across the sky or left to dwell in any direction to observe the fading rates of echoes within a small cone of angles. With the beam held stationary, the time scale associated with deep fading of F-region echoes is usually more than 5 min. This is consistent with the focusing and defocusing effects caused by the passage of ever-present medium-scale travelling ionospheric disturbances (TIDs). On occasion the time scale for deep fading is much shorter, of the order of tens of seconds or less, and this is thought to be due to the interference of many echoes from within the beam of the radar. It is shown that the echoes are not due to scatter from fine structure in the F-region, but rather due to the creation of multiple F-region paths with differing phase lengths by small, refracting irregularities in underlying, transparent spread sporadic-E, (Spread-E_s). The natural drift of the Spread-E_s causes the phase paths of the different echoes to change in different ways causing the interference.Two methods are used to investigate the rapidly fading F-region signals. Doppler sorting of the refracted F-region signal does not resolve echoes in angle of arrival suggesting that many echoes exist within a Fresnel zone [Whitehead and Monro (1975), J. atmos. terr. Phys. 37, 1427]. Statistical analysis of F-region amplitude data indicates that when the range spread in E_s is severe on ionograms, then a modified Rayleigh distribution caused by the combination of 10 or so echoes is most appropriate. Using knowledge of the refracting process the scale of E_s structure is deduced from these results. Both methods find a Spread-E_s irregularity size of the order of 1 km or less. It is proposed that the Rayleigh type F-region signals seen by Jacobsonet al. [(1991b), J. atmos. terr. Phys. 53, 63] are F-region signals refracted by spread-E_s.     

A comparison of the height of the maximum electron density of the F2-layer from real height analysis and estimates based on M(3000)F2

Estimates of the height of the F-layer peak based on formulations using the ionospheric transmission factor M(3000)F2 are compared with hmF2 derived from the real height analysis of digital ionograms acquired at a mid-latitude station. Based on the analysis of 27 hours of quiet data, our result shows that the M(3000)F2 methods are highly accurate and that the formulation developed by Bradley P. A. and Dudeney J. R., (1973, J. atmos. terr. Phys. 35, 2131) is most accurate.     

What determines the latitudinal extent of the auroral acceleration region?

Characteristic scales associated with auroral precipitation are investigated on the basis of quasistatic magnetotail models, resistive MHD simulations of magnetotail dynamics, and a general relation between parallel electric fields and velocity shear. Since the inverted-V precipitation region of discrete auroras (on the dusk side) is associated with upward flowing, region 1, currents, we investigate the distribution of these currents first. The overall distribution of region 1 type field-aligned currents and their dynamic changes can be explained by characteristic scales in the magnetotail and their mapping to the ionosphere. The quiet time region 1 currents are associated with the decrease of tail flaring. Their overall extent in the north-south direction is closely related to the scale height of the cross-tail current. Dynamic region 1 currents are related to the velocity shear of earthward flow, which can be generated by a tail instability. In that case the peaks of the enhanced region 1 currents are found to map closer to midnight and to lower latitudes than the quiet region 1 currents, consistent with average observations [Iijima and Potemra (1976a), J. geophys. Res.81, 2165]. On the basis of a general relation between parallel electric fields and ‘slippage’ in the plasma transport [Hesse and Schindler (1988), J. geophys. Res.93, 5559; Schindleret al. (1991), Astrophys. J.380, 293], we make estimates of the spatial extent of nonideal regions, where parallel electric fields may exist. For a plausible model of substorm reconfiguration, we find a latitudinal extent of about 7 km for a time scale of 1 min and a integrated parallel electric field of 5 kV. The length scale is proportional to the time scale. The sign of this parallel electric field is consistent with downward acceleration of electrons on the dusk side. The spatial extent of the parallel electric field region is independent of the microscopic generation mechanism if the time scale and the characteristic parallel potential difference (i.e. the integrated parallel electric field) are independent of this mechanism.     

The effect of vertical drift on the equatorial F-region stability

Owing to the high conductivity along magnetic field lines, the stability of the night-time equatorial F-region is determined by magnetic field line integrated quantities. However, slow vertical diffusion near the magnetic equator plus the rapid increase in ion chemistry rates at lower altitude combine to give a very small positive scale height for the electron concentration on the bottomside of the region. As a result, the field line averaged quantities are reasonably approximated by their equatorial values, provided that the E-region does not contribute significantly. The time-dependent behavior of the growth rate for the Rayleigh-Taylor gravitational instability on the F-region bottomside is examined here as a function of the vertical E × B drift velocity using reasonable chemistry to obtain approximate equatorial vertical profiles of ionospheric parameters. It is found that the growth rate exceeds the chemical recombination rate over most of the bottomside F-layer even without vertical drift, but that a realistic E × B drift can result, after about 1 h, in an increase of this growth rate by an order of magnitude. The absolute growth rate is so small (< 10⁻³ s⁻¹) with zero vertical drift that a seeding mechanism would probably be required for the formation of bubbles. The rapid appearance of bubbles shortly after sunset appears likely only after a period of upward drift, as is observed.     

Coherent-array HF Doppler sounding of traveling ionospheric disturbances: I. Basic technique

We present an introduction to the use of phase-coherent, multi-receiver HF Doppier sounding arrays for measuring the horizontal velocity of traveling ionospheric disturbances (TID's). The point of departure is the theorem of Pfister (1971, J. atmos. terr. Phys. 33, 999) relating ray Doppler to ray zenith angle for a monostatic full reflection sounder. Retaining the simple model of a specular, smooth ionospheric reflector which is deformed by a propagating undulation, we first generalize the theorem to bistatic sounding geometry and then include the effects of amplitude in addition to phase. Next, these results are cast into an algorithm for treating multi-receiver phase sounders containing many diverse baselines, in order to obtain an accurate and unambiguous solution in the plane of wave slowness (inverse of velocity). The point spread function of this solution is controlled by process bandwidth and by array geometry. We illustrate the coherent-array approach using data from an eight receiver array during passage of a TID.     

A new role for the plasmaphere in “quiet” ionospheric electrodynamics

Global scale longitudinal gradients of pressure in the plasmasphere may be formed naturally by ionospheric processes, or caused by electrostatic fields of ionospheric dynamo origin. It is shown that plasmaspheric gradients of pressure, orthogonal both to the magnetic field (B) and to grad B, generate geophysically significant field-aligned currents. Considering the ionosphere and plasmasphere as a coupled electrodynamic system, these currents alter non-negligibly the self-consistent ionospheric electric field and current. Criteria are established for this coupling mechanism (a kind of plasmaspheric impedance) to be significant. This has implications for the relationships of ionospheric electric fields and currents, F-region drifts, and magnetic variations, due to upper atmosphere tides and winds.     

Measurements of gradients in ionospheric parameters with a new nine-position experiment at Millstone Hill

A new nine-position experiment is now routinely carried out with the Millstone Hill incoherent scatter radars which allows estimation of spatial gradients in the measured ionospheric scalar parameters N_e, T_e, and T_i, and in the components of the ion velocity vector v_i. Use of this technique results in improved estimates of basic and derived parameters from incoherent scatter data at times of significant gradients. We detail the data analysis method and present the first results from this new experiment. The gradients in N_e and in the components of vi are used to compute the motion term in the ionospheric F region continuity equation ▿ · (Nv), which is then combined with ∂N/∂t to estimate the O⁺ recombination rate β at night. Meridional neutral winds U_mer are computed from the field-aligned ion velocity v_∥ and a calculation of the O⁺ diffusion velocity v_d, and it is found that horizontal gradients in the ion velocity field at times significantly affect the calculation of the neutral winds.     

Amplitude statistics of signals reflected from the ionosphere

Statistical analysis methods used to define the amplitude distributions of signals returned from the ionosphere are discussed in this paper. Emphasis is placed on determining accurately the parameter B, which is the ratio of steady to random components present in a signal. Thus B > 1 if the signal is dominated by the steady component, and B < 1 when the random components dominate. This study investigates the characteristics of B for F-region and E-region ionospheric echoes, as well as some types of spread-F, observed at the southern mid-latitude station Beveridge (37.3 S and 144.6 E). The results indicate that amplitude measurements obtained in approximately 100 s are adequate for determining B. The results also illustrate some effects that the E-region can have on F-region echoes.It is found that frequency spreading, the most common type of spreading observed at Beveridge, displays strong specular reflections and some signal variation due to interference at the leading edge of the F-region echo (i.e. B > 2). Within the spread echo B fluctuates between 0 and about 1.5 but is typically less than 1. The autocorrelation function of signal amplitude has a relatively large coherence interval, suggesting that this type of spread-F is due to interference of specular reflections from coherent irregularity structures with horizontal scale sizes of tens of kilometres rather than scattering from small scale irregularities. A second form of spread-F which would generally be classified as frequency spreading on standard ionoerams is actually due to off-vertical reflections from patches ol irregularities which originate south (poleward) of Beveridge. Echoes within this oblique spread-F (OS-F) do not exhibit coherence indicating that the irregularities responsible are of a smaller scale than those producing normal frequency spread. Finally, the phenomenon of spreading occurring on the second hop, but not the first hop trace is studied. It is shown that the form of the second hop echoes can be reproduced using a simple geometric model of ground scatter. The interpretation is supported by the fact that B for spread second hop echoes is less than 1 whereas it is much greater than 1 for the corresponding first hop echoes.     

Ionospheric conductivity dependence of the cross-polar cap potential difference and global Joule heating rate

We examine the extent to which the cross-polar cap potential difference ϕ and the global Joule heating rate, U, both determined by the magnetogram-inversion method (Kamideet al., 1981, J. geophys. Res. 86, 801), depend upon the assumed conductance models. For this purpose two statistically-determined conductance models developed by Siroet al. (1982, J. geophys. Res. 87, 8215) and ahn et al. (1983b, Planet. Space Sci. 31, 641), and a realistic conductance distribution estimated from bremsstrahlung X-ray image data (Ahnet al., 1989, J. geophys. Res. 94, 2565) have been used. As expected from earlier studies, U is less affected by the choice of conductance models than is ϕ. This is because U is a globally integrated quantity, and thus the local structures of the electric potential pattern do not affect it appreciably, whereas they are crucial in determining ϕ, which is defined as the difference between the maximum and minimum potential values usually found in the dawn and dusk sectors, respectively. A comparison between Uand ϕ based on the statistical conductance models and U and ϕ based on a realistic conductance distribution shows that there are considerable similarities, thus enabling us to use statistical conductance models as a first approximation in deriving such global quantities as the cross-polar cap potential difference and the global Joule heating rate in the study of solar wind-magnetosphere coupling. Several suggestions are made for improving the present available conductance models and some limitations (possibly intrinsic ones) are also discussed.     

An assessment of the effect of gravity waves on the width of radar Doppler spectra

Radars can be used to obtain turbulence parameters by measuring the width of the Doppler spectrum of returned power. Other effects can contribute to the Doppler-spectrum width, including short-period gravity waves, making turbulence parameter measurements more difficult. In this paper, an experimental study of the effect of gravity waves on the width of the Doppler spectrum is presented. The data were obtained using the Poker Flat 50 MHz VHP radar. A parameter Y_i is used to describe the discrepancy between the width of spectra sampled over a long period of time and that taken over a shorter time. If Y_i is not significantly different from 1.0, no contamination is present. The experimental data considered were of a time resolution that allowed the period and amplitude of the contaminating gravity wave to be determined. A theoretical expression for gravity wave contamination proposed by Hocking [(1988) J. geophys. Res.93, 2475–2491] was tested and found to agree with measurements. It was also found that non-unity values of Y_i occurred in some cases. This suggests that, at commonly used sampling times, short-period gravity waves can contaminate spectral width estimates.     

Fractal analysis of gravity wave spectra in the middle atmosphere

Wind fluctuations in the middle atmosphere behave like colored noise processes. They have a continuum of scales without dominant features and a power spectrum density (PSD) that often decays with frequency ƒ as ƒ^−β. Spectral index β is generally obtained through least-square fit to PSD estimated by Fourier methods. Graphs of colored noise have fractal plane-filling properties depending on β. An efficient method for finding β using the fractal dimension (D), based on analysis of 1/ƒ noise in galactic X-ray luminosities by McHardy I. and Czerny B., (1987, Nature325, 696), is described. An empirical relation is found between D and β and its validity is confirmed in limiting cases. Then D is obtained from power-law dependence of a length metric L(μ) on scale μ. The method is applied to middle-atmospheric velocity data from the Poker Flat radar in Alaska. Variations of D follow those in β, from an earlier analysis by Bemraet al., (1986, Handbook for MAP20, 216), but show an offset of 0.1–0.2 even after corrections for outliers, gaps, and additive noise. Usefulness of this method for screening data as an aid to spectral analysis is examined.     

Radiative perturbation due to the eruption of El Chichón: Effects on ozone

The ozone depletion over the Antarctic region is now attributed to processes involving heterogeneous chemistry on polar stratospheric clouds. Similar mechanisms are probably working also in the Northern hemisphere high latitudes [Douglass and Stolarski (1989) Geophys. Res. Lett. 16, 131] and may be important in explaining the secular trend of ozone in the last twenty years above 50° North [Pitari and Visconti (1991) J. geophys. Res. 96, 10,931]. Hofmann and Solomon [(1989) J. geophys. Res. 94, 5029] have shown that the local observed decrease in the ozone amount following the eruption of El Chichón could be explained in terms of heterogeneous chemistry on the volcanic aerosol surface. In this paper we use a two dimensional model to study the effects on ozone introduced by the El Chichón aerosols through a perturbation in the radiation field; both the temperature and the photolysis rates are affected. We show that up to half of the observed decrease may be attributed to radiative effects at mid latitudes.     

Computer simulations of the seasonal variations of the ionospheric equatorial anomaly in East Asia under solar minimum conditions

The previous dynamical, computer simulation model of the ionosphere at low latitudes of Chan H. F. and Walker G. O. (1984a, J. atmos. terr. Phys. 46, 1103; 1984b, J. atmos. terr. Phys. 46, 1113) has been modified to (1) include photoionization of molecular species NO⁺, N₂⁺ and O₂⁺ below 300km, (2) decouple the ionization and wind calculations below 180 km and (3) expand the geographical coverage to 46°N-30°S latitude. The first two modifications improved the model stability and the latter reduced the effect of the lateral boundaries on the equatorial anomaly. Results are presented for the representative seasonal months of January, April and July for East Asia, during solar minimum, comprising latitudinal-local standard time (120°E) contour plots of (1) the atmospheric pressure, (2) the computed meridional wind at 300 km, (3) the foF2 and (4) hmF2, together with latitudinal profiles of foF2 and N_T (electron content) showing the daytime development and nighttime decay of the equatorial anomaly.Comparisons have been made between the computer simulations and various experimental measurements of foF2, M(3000) F2 and N_T obtained in East Asia during periods of low solar activity. Most of the gross features of the development and decay of the equatorial anomaly at the various seasons were reproducible by the model simulations, the best agreement occurring for the equinoctial month of April.     

Calculation of auroral Bahner volume emission height profiles in the upper atmosphere

Energetic protons entering the atmosphere will either travel as auroral protons or as neutral hydrogen atoms due to charge-exchange and excitation interactions with atmospheric constituents. Our objective is to develop a simple procedure to evaluate the Balmer excitation rates of H_α and H_β, and produce the corresponding volume emission rates vs height, using semi-empirical range relations in air, starting from proton spectra observed from rockets above the main collision region as measured by Reasoneret al. [(1968) J. geophys. Res.73, 4185] and Søbraaset al. [(1974) J. geophys. Res.79, 1851]. The main assumptions are that the geomagnetic field is parallel and vertical, and that the pitch angle of the proton/hydrogen atom is preserved in collisions with atmospheric constituents before being thermalized. Calculations show that the largest energy losses occur in the height interval between 100 and 125 km, and the corresponding volume emission rate vs height profiles have maximum values in this height interval. The calculted volume emission rate height profile of H_β compares favorably with that measured with a rocket-borne photometer.     

Applying weakly nonlinear internal wave theories to solitary waves in the atmosphere

The theory of weakly nonlinear internal solitary waves is summarized in a simple way, with the view to applying it to solitary waves in the atmosphere. Two observations [Smith and Morton (1984) Australian Meteor. Mag. 33, 185; and Lin and Goff (1988) J. atmos. Sci. 45, 194] are considered in more detail. It is shown that for mesoscale solitary waves compressibility is important, and that the so-called ‘Morning Glory’ waves may possibly be described by shallow-fluid as well as deep-fluid solitary wave theory.     

On VLF radio wave reflection from distant mountain ranges—theory

We present an analysis for the reflection or scattering of VLF radio waves by gently sloping parallel ridges that may be well displaced from the great circle path between the transmitter and receiver antennae. It is shown that, under certain conditions, a spatial harmonic of the transverse profile of the terrain will produce a secondary signal that could be not far below the direct or primary signal. Such a resonant scattering mechanism may explain some of Thomson's [(1989), J. atmos. terr. Phys. 51, 339] observations in Dunedin, New ZeaLond.     

Polar thermospheric Joule heating,and redistribution of recombination energy in the upper mesosphere

Kellogg, W. W. (1961, J. Met. 18, 373) suggested that transport of atomic oxygen from the summer into the winter hemisphere and subsequent release of energy by three body recombination, O + O + N₂→O₂ + N₂ + E, may contribute significantly to the so-called mesopause temperature anomaly (increase in temperature from summer to winter). Earlier model calculations have shown that Kellogg's mechanism produces about a 10% increase in the temperature from summer to winter at 90 km. This process, however, is partly compensated by differential heating from absorption of UV radiation associated with dissociation of O₂. In the auroral region of the thermosphere, there is a steady (component of) energy dissipation by Joule heating (with a peak near 130 km) causing a redistribution and depletion of atomic oxygen due to wind-induced diffusion. With the removal of O. latent chemical energy normally released by three body recombination is also removed, and the result is that the temperature decreases by almost 2% near 90 km. Through dynamic feedback, this process reduces the depletion of atomic oxygen by about 25% and the temperature perturbation in the exosphere from 10% to 7% at polar latitudes. Under the influence of the internal dynamo interaction, the prevailing zonal circulation in the upper thermosphere (small in magnitude) changes direction when the redistribution of recombination energy is considered. The above described effects are very sensitive to the adopted rates of eddy diffusion. They are also strongly time dependent and are significantly reduced for disturbances associated with magnetic storms.     

Mechanisms for vertical separation of ions in sporadic-E layers

A model of the ionospheric E-region between 90 and 130 km altitude is constructed with normal molecular ions and two species of metal ion with different masses. This paper investigates whether the vertical structure observed in sporadic-E layers can be accounted for by separation of different ion species according to their mass. The result of the investigation is substantially negative. Another mechanism for range spread sporadic-E has signatures that may be sought in observational data.